Geometry Chapter 4: Classifying Triangles

Questions and Answers

What is an Acute Triangle?

One right angle

One obtuse angle

Three acute angles (correct)

Three right angles

What defines an Equiangular Triangle?

Three congruent sides

Three congruent acute angles (correct)

Three angles measuring 90 degrees

One right angle

What characterizes a Right Triangle?

No right angles

Three acute angles

One right angle (correct)

Three obtuse angles

What is an Obtuse Triangle?

One obtuse angle Signup and view all the answers

What defines an Equilateral Triangle?

Three sides of equal length Signup and view all the answers

What characterizes an Isosceles Triangle?

At least two sides are congruent Signup and view all the answers

What is a Scalene Triangle?

No congruent sides Signup and view all the answers

What is the definition of Interior in a triangle?

The set of all points inside the figure. Signup and view all the answers

What is the definition of Exterior in a triangle?

The set of all points outside the figure. Signup and view all the answers

What is an Interior Angle?

Formed by two sides of a triangle. Signup and view all the answers

What is an Exterior Angle?

Formed by one side of the triangle and the extension of an adjacent side. Signup and view all the answers

What is a Remote Interior Angle?

An interior angle that is not adjacent to the exterior angle. Signup and view all the answers

What does the Exterior Angle Theorem state?

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. Signup and view all the answers

What does the Third Angles Theorem state?

If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. Signup and view all the answers

Study Notes

Triangle Classifications

Acute Triangle: Contains three acute angles, each less than 90 degrees.
Equiangular Triangle: Features three congruent acute angles, thereby also being an acute triangle.
Right Triangle: Characterized by having one right angle, equal to 90 degrees.
Obtuse Triangle: Contains one obtuse angle, which is greater than 90 degrees but less than 180 degrees.
Equilateral Triangle: Distinguished by having three congruent sides and angles, each measuring 60 degrees.
Isosceles Triangle: Comprises at least two congruent sides and the angles opposite those sides are also congruent.
Scalene Triangle: No sides or angles are congruent, making all sides and angles different in measurement.

Angle Definitions

Interior: Refers to all points located within the triangle itself.
Exterior: Comprises all points that lie outside the triangle.

Angle Relationships

Interior Angle: Formed by the intersection of two sides of the triangle.
Exterior Angle: Created by one side of the triangle and the extension of an adjacent side.
Remote Interior Angle: An interior angle that is not adjacent to the corresponding exterior angle.

Theorems

Exterior Angle Theorem: States that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Third Angles Theorem: Indicates that if two angles of one triangle are congruent to two angles of another triangle, then the third angles in both triangles are also congruent.

Description

This quiz focuses on the classification of triangles, covering various types such as acute, equiangular, right, obtuse, equilateral, and isosceles triangles. Each flashcard provides definitions and characteristics of these triangle types. Test your knowledge of triangle properties in this engaging quiz.